Yes, that's definitely what it's about and what you've described is classic hypercorrection showing that the speaker is using a variety she/he's not comfortable with, which leads to the conclusion that David Cameron is not using his first language when speaking here. There's good experimental evidence about the different responses to 'I and David' etc. Even stronger evidence that the 'David and I' 'rule' is unnatural in some way is that 'David and we' and 'David and he' are less acceptable than 'David and I'. Will post more references later (off to teach now) B--)